Ask HN: The most CPU and memory at the lowest cost?

We are considering building our own scrappy big data cluster but want to do this at an extreme low budget. Since it will only be used by our own internal data sciences team for analysis and experimentation, we don't need crazy redundancy or production grade hardware.

So, does anyone have any suggestions on cheap, even consumer grade, hardware to buy and squeeze the most CPUs and memory into a low budget and ideally the smallest space?

Would just stacking a bunch of micro ATX/mini-ITX boards make sense (maybe even without cases) screwed to some boards we can rack? We probably new a few terabytes of memory so maybe the limited memory slots will be a shortcoming.

Has anyone here done this? None of us are necessarily hardware pros.